The equation of wave motion is $Y = 5 \sin (10 \pi t - 0.02 \pi x + \pi / 3)$ where $x$ is in $m$ and $t$ is in $s$. The velocity of the wave is (in $m/s$)

The displacement due to a wave moving in the positive $x$-direction is given by $y = \frac{1}{(1 + x^2)}$ at time $t = 0$ and by $y = \frac{1}{[1 + (x - 1)^2]}$ at $t = 2$ seconds,where $x$ and $y$ are in metres. The velocity of the wave in $m/s$ is

The figure represents the instantaneous picture of a transverse harmonic wave travelling along the negative $x$-axis. Identify the correct statement(s) related to the movement of the points shown in the figure. The points moving opposite to the direction of propagation (i.e., moving in the negative $y$-direction) are:

The displacement of a wave is expressed as $x(t) = 5 \cos \left(628 t + \frac{\pi}{2}\right) \text{ m}$. The wavelength of the wave when its velocity is $300 \text{ m/s}$ is: (in $\text{ m}$)

The equation of a sound wave is $y = 0.0015 \sin (62.4 x + 316 t)$. Find the wavelength of this wave.

What is the ratio of the amplitudes of the waves $y_1 = 10 \sin(3\pi t + \frac{\pi}{3})$ and $y_2 = 5[\sin 3\pi t + \sqrt{3} \cos 3\pi t]$?